Determine if the following sequences represent an A.P., assuming that the pattern continues. If it is an A.P., find the nth term:
2, 2, 2, 2, ...
Formula Used.
dn = an + 1 – an
an = a + (n–1)d
In the above sequence,
a = 2;
d1 = a2–a1 = 2–2 = 0
d2 = a3–a2 = 2–2 = 0
d3 = a4–a3 = 2–2 = 0
⇒ As in A.P the difference between the 2 terms is always constant
The difference in sequence comes to be 0.
∴ The above sequence is not an A.P
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